161 research outputs found
Low-complexity computation of plate eigenmodes with Vekua approximations and the Method of Particular Solutions
This paper extends the Method of Particular Solutions (MPS) to the
computation of eigenfrequencies and eigenmodes of plates. Specific
approximation schemes are developed, with plane waves (MPS-PW) or
Fourier-Bessel functions (MPS-FB). This framework also requires a suitable
formulation of the boundary conditions. Numerical tests, on two plates with
various boundary conditions, demonstrate that the proposed approach provides
competitive results with standard numerical schemes such as the Finite Element
Method, at reduced complexity, and with large flexibility in the implementation
choices
Blind calibration for compressed sensing by convex optimization
We consider the problem of calibrating a compressed sensing measurement
system under the assumption that the decalibration consists in unknown gains on
each measure. We focus on {\em blind} calibration, using measures performed on
a few unknown (but sparse) signals. A naive formulation of this blind
calibration problem, using minimization, is reminiscent of blind
source separation and dictionary learning, which are known to be highly
non-convex and riddled with local minima. In the considered context, we show
that in fact this formulation can be exactly expressed as a convex optimization
problem, and can be solved using off-the-shelf algorithms. Numerical
simulations demonstrate the effectiveness of the approach even for highly
uncalibrated measures, when a sufficient number of (unknown, but sparse)
calibrating signals is provided. We observe that the success/failure of the
approach seems to obey sharp phase transitions
Listening to features
This work explores nonparametric methods which aim at synthesizing audio from
low-dimensionnal acoustic features typically used in MIR frameworks. Several
issues prevent this task to be straightforwardly achieved. Such features are
designed for analysis and not for synthesis, thus favoring high-level
description over easily inverted acoustic representation. Whereas some previous
studies already considered the problem of synthesizing audio from features such
as Mel-Frequency Cepstral Coefficients, they mainly relied on the explicit
formula used to compute those features in order to inverse them. Here, we
instead adopt a simple blind approach, where arbitrary sets of features can be
used during synthesis and where reconstruction is exemplar-based. After testing
the approach on a speech synthesis from well known features problem, we apply
it to the more complex task of inverting songs from the Million Song Dataset.
What makes this task harder is twofold. First, that features are irregularly
spaced in the temporal domain according to an onset-based segmentation. Second
the exact method used to compute these features is unknown, although the
features for new audio can be computed using their API as a black-box. In this
paper, we detail these difficulties and present a framework to nonetheless
attempting such synthesis by concatenating audio samples from a training
dataset, whose features have been computed beforehand. Samples are selected at
the segment level, in the feature space with a simple nearest neighbor search.
Additionnal constraints can then be defined to enhance the synthesis
pertinence. Preliminary experiments are presented using RWC and GTZAN audio
datasets to synthesize tracks from the Million Song Dataset.Comment: Technical Repor
Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm
In phase retrieval, the goal is to recover a complex signal from the
magnitude of its linear measurements. While many well-known algorithms
guarantee deterministic recovery of the unknown signal using i.i.d. random
measurement matrices, they suffer serious convergence issues some
ill-conditioned matrices. As an example, this happens in optical imagers using
binary intensity-only spatial light modulators to shape the input wavefront.
The problem of ill-conditioned measurement matrices has also been a topic of
interest for compressed sensing researchers during the past decade. In this
paper, using recent advances in generic compressed sensing, we propose a new
phase retrieval algorithm that well-adopts for both Gaussian i.i.d. and binary
matrices using both sparse and dense input signals. This algorithm is also
robust to the strong noise levels found in some imaging applications
Balancing Sparsity and Rank Constraints in Quadratic Basis Pursuit
We investigate the methods that simultaneously enforce sparsity and low-rank
structure in a matrix as often employed for sparse phase retrieval problems or
phase calibration problems in compressive sensing. We propose a new approach
for analyzing the trade off between the sparsity and low rank constraints in
these approaches which not only helps to provide guidelines to adjust the
weights between the aforementioned constraints, but also enables new simulation
strategies for evaluating performance. We then provide simulation results for
phase retrieval and phase calibration cases both to demonstrate the consistency
of the proposed method with other approaches and to evaluate the change of
performance with different weights for the sparsity and low rank structure
constraints
Convex Optimization Approaches for Blind Sensor Calibration using Sparsity
We investigate a compressive sensing framework in which the sensors introduce
a distortion to the measurements in the form of unknown gains. We focus on
blind calibration, using measures performed on multiple unknown (but sparse)
signals and formulate the joint recovery of the gains and the sparse signals as
a convex optimization problem. We divide this problem in 3 subproblems with
different conditions on the gains, specifially (i) gains with different
amplitude and the same phase, (ii) gains with the same amplitude and different
phase and (iii) gains with different amplitude and phase. In order to solve the
first case, we propose an extension to the basis pursuit optimization which can
estimate the unknown gains along with the unknown sparse signals. For the
second case, we formulate a quadratic approach that eliminates the unknown
phase shifts and retrieves the unknown sparse signals. An alternative form of
this approach is also formulated to reduce complexity and memory requirements
and provide scalability with respect to the number of input signals. Finally
for the third case, we propose a formulation that combines the earlier two
approaches to solve the problem. The performance of the proposed algorithms is
investigated extensively through numerical simulations, which demonstrates that
simultaneous signal recovery and calibration is possible with convex methods
when sufficiently many (unknown, but sparse) calibrating signals are provided
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